SU(2)-Cyclic Surgeries on Knots. (24th November 2015)

• Record Type: Journal Article
• Authors: Lin, Jianfeng
• Is Part Of: International mathematics research notices. Volume 2016:Number 19(2016)
• Page Start: 6018
• Page End: 6033
• Publication Date: 2015-11-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnv326
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract : A surgery on a knot in $S^{3}$ is called ${\rm SU}(2)$ -cyclic if it gives a manifold whose fundamental group has no noncyclic ${\rm SU}(2)$ representations. Using holonomy perturbations on the Chern–Simons functional, we prove that two ${\rm SU}(2)$ -cyclic surgery coefficients $\frac {p_{1}}{q_{1}}$ and $\frac {p_{2}}{q_{2}}$ should satisfy $|p_{1}q_{2}-p_{2}q_{1}|\leq |p_{1}|+|p_{2}|$ . This is an analog of Culler–Gordon–Luecke–Shalen's cyclic surgery theorem.